IlocA: An algorithm to Cluster Cells and form Imputation Groups from a pair of Classification Variables

We set out the novel bottom up procedure to aggregate or cluster cells with small frequency counts together, in a two way classification while maintaining dependence in the table. The procedure is model free. It combines cells in a table into clusters based on independent log odds ratios. We use this procedure to build a set of statistically efficient and robust imputation cells, for the imputation of missing values of a continuous variable using a pair classification variables. A nice feature of the procedure is it forms aggregation groups homogeneous with respect to the cell response mean. Using a series of simulation studies, we show IlocA only groups together independent cells and does so in a consistent and credible way. While imputing missing data, we show IlocAs generates close to an optimal number of imputation cells. For ignorable non-response the resulting imputed means are accurate in general. With non-ignorable missingness results are consistent with those obtained elsewhere. We close with a case study applying our method to imputing missing building energy performance data